A261830 Decimal expansion of Integral_{0..1/2} log(gamma(x+1)) dx (negated).

0, 4, 2, 8, 5, 3, 7, 4, 0, 6, 5, 0, 2, 9, 0, 9, 4, 4, 5, 5, 6, 6, 2, 3, 0, 4, 0, 5, 5, 6, 1, 9, 9, 1, 9, 0, 2, 9, 7, 4, 7, 5, 9, 3, 2, 1, 2, 3, 4, 4, 3, 8, 8, 0, 7, 4, 0, 3, 4, 2, 4, 4, 2, 0, 3, 1, 4, 9, 9, 1, 4, 7, 7, 7, 0, 0, 8, 8, 6, 7, 9, 6, 3, 3, 1, 8, 3, 3, 3, 5, 6, 3, 9, 6, 5, 3, 2, 2, 3, 6, 3, 3, 3

Offset

0,2

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.15 Glaisher-Kinkelin constant, p. 135.

Links

Table of n, a(n) for n=0..102.

Formula

-1/2-(7/24)*log(2)+(1/4)*log(Pi)+(3/2)*log(A), where A is the Glaisher-Kinkelin constant 1.282427... (A074962).

Example

-0.042853740650290944556623040556199190297475932123443880740342442...

Mathematica

Join[{0}, RealDigits[-1/2 - (7/24)*Log[2] + (1/4)*Log[Pi] + (3/2) * Log[Glaisher], 10, 102] // First]

Prog

(PARI) -intnum(x=1, 3/2, lngamma(x)) \\ Charles R Greathouse IV, Apr 18 2016

Crossrefs

Cf. A074962.

Sequence in context: A066104 A143095 A141073 * A194038 A131819 A194064

Adjacent sequences: A261827 A261828 A261829 * A261831 A261832 A261833

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Sep 02 2015

Status

approved